Periodic solutions for a class of diffusive Nicholson’s blowflies model with Dirichlet boundary conditions

Bingwen Liu,Weidong Jiao,Junxia Meng

doi:10.1186/1029-242x-2013-449

Abstract

Abstract In this paper, we study the problem of periodic solutions for a class of diffusive Nicholson’s blowflies model with Dirichlet boundary conditions. By applying the Schauder fixed point theorem, the existence of nontrivial nonnegative periodic solutions of the considered model is established. Our results complement with some recent ones. MSC:35B05, 35B10.

Highlights

The effects of the periodic environment on evolutionary equations with delays have been the object of intensive analysis by numerous authors, some of the results can be found in [ – ] and the references therein
1 Introduction In the classic study of population dynamics, Gurney et al [ ] proposed the following delay equation: du(t) = –δu(t) + pu(t – τ )e–au(t–τ) dt to describe the population of the Australian sheep-blowfly Lucilia cuprina, where u(t) is the population of the adult flies at the time t, p is the maximum per capita daily egg production rate, /a is the size at which the blowfly population reproduces at its maximum rate, δ is the per capita daily egg adult death rate, and τ is the maturation time
3 Main result and its proof The purpose of the present section is to prove the existence of a nonnegative periodic solution u(t, x) of ( . )-( . )

Summary

Introduction

The effects of the periodic environment on evolutionary equations with delays have been the object of intensive analysis by numerous authors, some of the results can be found in [ – ] and the references therein. The authors in [ ] obtained the existence of periodic solutions for the following nonlinear diffusive Nicholson’s blowflies model with constant delays and constant coefficients: ∂t t–τ the existence of periodic solutions for the diffusive Nicholson’s blowflies model with time-varying coefficients and delays has not been sufficiently researched.

Results

Conclusion